Mirror selection but maintain current selection
This may not be the best solution, but I have found that it works. Start by going into Edit Mode, make sure you've opened the Object Data tab of the Properties Panel (1), then create a vertex group for the initial selection of vertices. Create the new group by pressing the + sign to the right (2), and include the selected vertices by clicking the "Assign" button (3).



Next, while still in Edit Mode, locate the "Select" Menu at the top left of the 3D-View, and open it to choose the "Mirror Selection" option at the bottom of that menu.



Finally, go back to the Vertex Group you created and press the "Select" button to get back your original selection.